An Indoor Air Quality Model for Particulate Matter
Leslie E. Sparks, U. S. Environmental Protection Agency, Office of Research and
Development, National Risk Management Research Laboratory, Air Pollution
Prevention and Control Division, Research Triangle Park, NC 27711
ABSTRACT
The standard for particulate matter (PM) less than 2.5 jim in aerodynamic diameter
(PM2j) proposed by the U.S. EPA has produced considerable interest in indoor exposures
to PM. Indoor air quality (LAQ) models provide a useful tool for analyzing both the
indoor exposure to PM and the impact of risk management options on exposure. Because
analysis of the impact of PM exposures requires analysis over a particle size distribution,
most existing IAQ models, which are designed to allow analysis of the impact of a single
pollutant component, are not well suited for analysis of PM exposure. To overcome this
limitation, a multicompartment IAQ model was developed for PM exposures for a full
particle size distribution. The model allows analysis of the effect of: the building shell on
the penetration of outdoor particles into the indoors, the deposition of particles to indoor
surfaces, particle removal by air cleaners, and indoor particle sources. The use of the
model is demonstrated by an analysis of both the time-varying impact of outdoor PM on
indoor PM levels and the effect of a central furnace filter on indoor PM concentrations.
INTRODUCTION
As a result of EPA's proposed standard for particulate matter (PM) less than 2,5 um in
aerodynamic diameter (PMi.;), a need for an indoor air quality (IAQ) model for PM has
developed. IAQ models have been developed for PM. However, they are usually single-
compartment models and treat only the steady state situation (see Thornburg et al.1 for a
discussion of some of these models). Existing multicompartment time-varying IAQ
models generally allow modeling of one pollutant2*3'4 and are thus unsuitable for
modeling PM where many of the effects are due to particle size distribution. These
single-pollutant models can be used to analyze PM by combining several model runs.
However, this is inefficient and error prone. The IAQ model described in this paper
allows analysis of the time-dependent behavior of up to eight different particle diameters
and includes the effects of particle air cleaners, outdoor PM concentrations, air exchange
rates, and PM sources.
THE MODEL
General equations
The new IAQ model is based on the multiroom IAQ model RISK4. The major changes
made to RISK to allow modeling of PM were:
• Particle size distribution was added,
• Particle deposition was added,
• Particle penetration through the building fabric was added,
• Particle sources were added,
• Time-varying outdoor concentration was added, and
• Air cleaner efficiency as a function of particle diameter was added.
-------
The new model is based on mass balance. The general mass balance equation for a
single pollutant or particle size for room i of N rooms is:
Equation 1. Mass balance equation for room i of N rooms.
j=N j=N
Vi~ = CaPtQaii + ChQhJ+ £ CjQjj-CiiQfr + Qifi)- £ CiQy + Si-Rt
j~l,j*i J=lJ*i
where Vj is the volume of room i; Q is the concentration in room i; Ca is the
concentration outdoors; Pt is the penetration factor for pollutants into the indoors; Qa,i is
the air flow from the outdoors into room i; Ch is the concentration leaving the heating,
ventilating, and air conditioning (HVAC) system; Qh,i is the air flow from the HVAC
system into room i; Q is the concentration in room j; Qjsi is the air flow from room j into
room i; Qj)8 is the air flow from room i to the outdoors; QJJ, is the flow from room i into
the HVAC system; Qy is the air flow from room i into room j; S; is the source term for
pollutants produced in room i; and Rj is the removal term for pollutants removed in room
i, including those removed by sinks and in-room air cleaners. Note that most of the terms
in Equation (1) may vary with time. In the model implemented here, Ca, the flow terms
Qa.ij Qh,i, and Qi j and the flows needed to balance them, and Sj are allowed to vary with
time. The penetration term, Pt, the source term, Sj, and the removal term, Rj, are
generally functions of particle diameter.
The term for the HVAC system is determined by the design of the HVAC system and the
location of filters in the system. In a commercial system where mechanical ventilation is
provided by the HVAC system, air is returned to the HVAC system from most rooms,
and air cleaners are located after the outdoor air and room air are mixed (see Figure 1).
The equation for the HVAC system is:
Equation 2. Equation for HVAC system.
i=N i=N
Ch /Qh,i + !/h^ = (l-WaQaJi + 0-
i=l i=l
where Vj, is the volume of the HVAC system, r\ is the efficiency of the air cleaner in the
HVAC system, and Qa>i, is the air flow from the outdoors into the HVAC system.
The volume of the HVAC system is generally very small relative to the building volume,
and the various air flow rates and the change of concentration with time in the HVAC
system can be neglected. The equation for the concentration leaving the HVAC system is
then:
-------
Equation 3. Final equation for HVAC system.
i-N
CA=-
i=N
Z
1=1
Figure 1. Diagram of two compartments with an HVAC system.
Roornj
QA,
In Figure 1, Qaj is the air flow from the outdoors into room j, Qj$a is the air flow from
room j to the outdoors, Q,-,h is the air flow from room j into the HVAC, and Qhj is the air
flow from the HVAC into room j.
For a typical residential system: heating and air conditioning (HAC) are provided, there is
no outdoor air entering the HAC system, air is returned to the HAC system from one
location, and the filter is typically located on the return side of the system (Figure 2).
The equation for the HAC system is then:
Equation 4. Equation for residential HAC system.
.2 Qh,i
where CT is the concentration at the return location and Qr>h is the air air flow from the
return location to the HVAC system. If outdoor air does enter a typical residential system
due to leaks in the system, the air is not cleaned and the resulting concentration is given
by:
-------
Equation 5. Equation for HAC system with outdoor air leakage into the system.
Figure 2. Two rooms with an HAC system.
The air entering a room from all locations must equal the air leaving the room to all
locations, the total amount of outdoor air entering the building must equal the total
amount of outdoor air leaving the building, and the total air entering the HVAC system
from all locations must equal the total air leaving the HVAC system to all locations.
Additional equations are necessary to describe the source and removal terms. The entire
system of equations is solved numerically using techniques described by Yamamoto et
al.5
Particle size distribution calculations
The model allows calculation of concentration for a maximum of eight different particle
diameters. The particle data are entered into the model using data entry tables. The user
enters the particle diameter and appropriate data for that diameter. If the user uses the
model defaults for penetration, particle deposition, or air cleaner efficiency, the user must
use the physical particle diameter. Because the PM2.5 standard is based on aerodynamic
diameter, the model provides an option to convert from physical diameter to aerodynamic
diameter using6:
Equation 6. Equation for converting between aerodynamic and physical diameter.
where dA is the particle aerodynamic diameter, d is the particle physical diameter, C is
the Cunningham correction factor, and p is the particle density. Particle concentration
-------
may be entered as number concentration, volume concentration, or mass concentration as
long as the same concentration units are used to describe all particle concentrations and
source emission rates.
Particle penetration
For particles, the penetration factor, Pt, is a function of particle diameter and is not well
known. Several studies of penetration have been reported in the literature, but there is no
consensus about the proper values to use. McMurry et a/.7 reported that the penetration
varied from 0.2 to 0.4 for particles with diameters between 0.01 and 0.1 um. Thatcher
and Layton8 reported that the penetration was unity for particles with diameters less than
10 um. Tung et a/.9reported an average penetration factor of 0.78 for particles with
aerodynamic diameters less than 10 jam (PMio) in an enclosed office. Thornburg et al.1
reported data and modeling showing that the penetration for a residence without an
HVAC system varied from 0.5 to 0.8 for particle diameters over the range of 0.02 to 8
um. It is difficult to compare these studies, because many authors do not define whether
their results are for particle aerodynamic or physical diameter.
The new model allows the user to enter values of penetration for various particle
diameters or the user may use default values provided by the model. The model defaults
are based on experiments conducted in EP A's IAQ research house at Research Triangle
Park, NC, literature values, and modeling. The default values, based on physical
diameter, are shown in Figure 3.
Figure 3. Default penetration as a function of particle physical diameter.
Ptrtfcfe physical dtam*(»t (pmj
Particle deposition
The deposition of particles onto indoor surfaces is a major loss mechanism for particles.
The loss of particles due to deposition can be described hi terms of deposition loss rate
with units of inverse hours or in terms of deposition velocity with units of meters per
-------
hour. The model uses deposition velocity with the loss of particles due to deposition
given by:
Equation 7. Equation for deposition losses of particles indoors.
where R
-------
the user to specify the emission rate for each particle diameter that is modeled. It is
critical that the units used to describe source emission rates be consistent with those used
to describe outdoor concentrations. For example, if outdoor concentrations are entered as
particles per cubic centimeter, then the source emission rate must be entered as particles
per hour per unit source. Results of ongoing research on indoor PM sources will be
incorporated into the model as soon as they become available.
Figure 4. Model default particle deposition velocity as a function of particle
physical diameter.
10 i
Sparte et al. (2000). chamber
Sparks et al. (2000), research house
Foghetal. (1897)
Byrne stai. (1995)
-Model default
0.01
0.1 1
Particle physical diameter (pffl)
Particle air cleaners
Air cleaners can have a significant impact on the indoor particle concentration. Because
of the large amount of air recirculated in many buildings, even relatively low efficiency
air cleaners can significantly reduce indoor particle concentrations. Any analysis of field
data should account for the effect of air cleaners.
Hanley et al.16 provide data on the efficiency of a wide range of particulate air cleaners.
These data have been extended with results from EPA's environmental technology
verification (ETV) program. Air cleaner efficiencies for several devices based on Hanley
et al. and the ETV data are shown in Figure 5 along with the typical particle physical
diameter range of some typical indoor air pollutants.
The model allows the user to enter air cleaner efficiency for the diameters used in the
model or the user can select model defaults for a range of air cleaners. The default air
cleaners and their efficiencies are shown in Figure 6.
-------
Figure 5. Air cleaner efficiencies as a function of particle physical diameter and
physical diameter range of typical indoor pollutants.
0-1
0.01
-X5
§ S S g
Q O QO
* ASHRAE 95% filler
• ASHRAE 85% filter
a. ASHRAE 65% filter
X ASHRAE 40% filter
o Furnace filter
• Electronic air cleaner
™-t»™ Bacteria
Pollens
• • •*• - - Environmental tobacco smoke
—O—Atmospheric aerosol
••Q—Pet allergens
•—Dust mites
Particle physical diameter (Mm)
Figure 6. Default air cleaner efficiencies as a function of particle physical diameter
provided by model.
0.1 1
Particle physical diameter (pm)
-------
COMPARISON OF MODEL AND MEASUREMENTS
Modeling impact of outdoor PM on indoor PM
One of the uses of the IAQ model is in analyzing the effects of outdoor PM on indoor
PM. The major parameters necessary for this analysis are the penetration of outdoor
particles into the indoors, the deposition of indoor particles, and the efficiency of any
indoor air cleaners. Several investigators, for example Thatcher and Layton8 and
Thornburg et al.1, have used a single-compartment steady-state model to analyze the
impact of outdoor PM on indoor PM. In many cases, the outdoor PM concentration
varies significantly with time and an analysis with a dynamic model is needed.
The analysis that follows is based on data collected in EPA's IAQ research house. The
research house is a typical three-bedroom ranch style house with a volume of 300 m3. The
house is unoccupied and unfurnished. The floor plan for the test house is shown in Figure
7. The house has central air conditioning and a natural gas central heating system. Exhaust
fans are provided in the hall bathroom and for the kitchen stove hood. The exhaust fans
were not operated during these experiments. The monitoring room, isolated from the rest
of the house, is not considered in any modeling. For these experiments the house was
operated with the HAC system fan on continuously and with the thermostat set to
maintain an indoor temperature of 22° C. The furnace filter was removed. Air flows
from the HAC into each room were measured as was the air flow from the hall to the
HAC return. The total HAC air flow was about 1,800 m3/h or 6 house volumes/h. All
interior doors were open for these experiments. Indoor PM was measured in the master
bedroom.
Indoor and outdoor particle size distributions were collected over the particle physical
diameter range of 0.015 to 7.5 um using a scanning mobility particle sizer (SMPS) for the
range of 0.015 to 0.6 um and a single-particle laser counter (Lasx) for the range of 0.1 to
7.5 urn. Indoor and outdoor data were collected using the same instrument. In general
the SMPS and the Lasx were in good agreement where their measurements overlapped.
The instruments sampled the outdoors for 30 minutes and then sampled the indoors for 30
minutes. An automatic valve was used to switch the sample from outdoors to indoors.
Even with 30-minute sampling, the number of particles with diameters larger than 3 um
was too low to provide valid count statistics.
The air exchange rate with the outdoors was determined using sulfur hexafluoride
SFe was injected periodically and the decay method was used to determine the air
exchange rate. A meteorology station at the research house provided data on wind speed,
wind direction, relative humidity, and outdoor temperature. Indoor temperature and
relative humidity were also measured.
The model calculated for particle physical diameters of 0.015, 0.05, 0.077, 0.1, 0.2, 0.35,
0.5, and 1.25 jim. The model default settings for penetration and deposition were used.
The measured air exchange rates were used in the modeling. The results are shown in
Figure 8.
-------
Figure 7. Floor plan of EPA's IAQ research house.
Several useful metrics can be used to compare quantitatively model predictions and
measurements. Some of the more useful are:
1. The average relative error between measurements and predictions given by:
Equation 10. Equation for the average absolute value of the relative difference
between predicted and measured concentrations.
n
2
i—I
where cpj is the value of the i* predicted concentration, c0j is the value of the ith observed
concentration, and n is the number of observations.
2. The normalized mean square error (NMSE) given by:
10
-------
Equation 11. Equation for normalized mean square error.
NMSE=(cp-c0)2'0.9
Normalized mean square error (NMSE) <0.25
Regression intercept (a) <25% of the average value of the
measurements
Regression slope (b) 0.75 to 1.25
Fractional bias (FB) Absolute value <0.25
Quantitative comparisons of the model predictions and experimental data are shown in
Table 2.
11
-------
Figure 8. Comparison between model predictions and research house data.
Model d=0.015pm
Model d=0.05 pm
Model d=0.077 pm
Model d=0,1 pm
Model d=0,2M
-------
and the data is due to uncertainty in the values of deposition rate and penetration factor.
Research is ongoing to provide better information on both of these factors.
Effect of furnace filter on indoor PM
An experiment with the furnace filter in place was conducted to determine if a common
furnace filter had an impact on indoor PM concentrations. Although the single-pass
efficiency of a furnace filter is low, the recirculation rate through the filter is about 6
house volumes per hour. Thus some effect could be expected. The comparison of
measurements and data for no filter is shown in Figure 9. The agreement between model
and data is poor.
The comparison between model predictions and data when the default values of furnace
filter efficiency are used is shown in Figure 10. The agreement between model and data
is greatly improved. This indicates that the effect of the furnace filter must be taken into
account when data are analyzed. In buildings with more efficient filtration, the effect of
the filter would be much greater.
Figure 9. Comparison of model predictions with no furnace filter and research
house data with a furnace filter.
- - •
•
D
0
*
•
o
el d=0.05
el d-0.1
»l d=0.2
1 d=Q 5
1 d * 1.25
d- 0.015
d-0.05
d-0.1 tJ
d"0.2 v
d*0.5 \i
d-1.25
ir
n
m
m
lim
Mm
m
m
13
-------
CONCLUSIONS
An IAQ model for PM has been developed. The model allows analysis of up to eight
different particle diameters at a time. When the default values of penetration and particle
deposition are used, the model predictions are in fair agreement with experimental data
from an IAQ research house for situations with and without a furnace filter in the HAC
system. The results of modeling measurement show that even a low efficiency filter has
an effect on the relationship between indoor and outdoor PM.
MODEL AVAILABILITY
The model is available from EPA's web site at:
http://www.epa. gov/docs/crb/iemb/index.htm
or on CD-ROM by contacting L. E. Sparks, Indoor Environment Management Branch,
Air Pollution Prevention and Control Division, National Risk Management Research
Laboratory, U. S. Environmental Protection Agency, MD-54, Research Triangle Park,
NC 27711. The model requires Windows 95 or 98 and at least 64 MB of RAM.
Figure 10. Comparison of model predictions with furnace filter and research house
data with furnace filter.
i. M
M
— — M
— -M
M
M
a D
* D
* D
» D
* D
o D
etiiG.G
delO-G
ef*I S t
delQ.2
delO.5
del 12
la D=0
la d = 0.
t«
-------
REFERENCES
1. Thomburg, J., Ensor, D. S., Rodes, C. E., Lawless, P. A., Sparks, L. E., and Mosley,
R. B., Penetration of particles into buildings and associated physical factors, Part I:
Model development and computer simulations, Aerosol Science and Technology,
2000 (In press).
2. Axley, J. W., Progress toward a general analytical method for predicting indoor air
pollution in buildings: Phase III Report. Report Number NBSIR 88-3814, National
Bureau of Standards, Gaithersburg, MD, 1988.
3. Dokka, T, H., Bj0rseth, O., and Hanssen, S. O., ENVISIM: a Windows application
for simulation of IAQ, Indoor Air 96 Proceedings of the 7th International Conference
on Indoor Air Quality and Climate, Nagoya, Japan, Vol. 2, 491-496,1996.
4. Sparks, L. E., IAQ Model for Windows RISK Version 1.0 User Manual, EPA-600/R-
96-037 (NTIS PB96-501929), Air Pollution Prevention and Control Division,
Research Triangle Park, NC, March, 1996.
5. Yamamoto, T., Ensor, D. S., Lawless, P. A., Damle, A. S., Owen, M. K., and Sparks,
L. E., Fast direct solution method for multizone indoor model, Proceedings Indoor
Air Modeling, Champaign, IL, 1988.
6. Calvert, S,, and Englund H. M., Handbook of Air Pollution Technology, John Wiley
and Sons, New York, NY, 1984.
7. MeMurry, P.H., Stanbouly, S. H., Dean, J.C., and Techman, K.Y., Air and aerosol
infiltration in homes, ASHRAE Transactions, 1985,91 A:255-263.
8. Thatcher, T.L., and Layton, D.W., (1995). Deposition, resuspension, and penetration
of particles within a residence, Atmospheric Environment, 1995,2P:1487-1497.
9. Tung, T.C.W., Chao, C.Y.H., and Burnett, J., A methodology to investigate the
particulate penetration coefficient through building shell, Atmospheric Environment,
1999,33:881-893.
10. Nazaroff, W. W., and Cass, G. R., Mathematical modeling of indoor aerosol
dynamics, Environmental Science and Technology, 1989, 23:157-166.
11. Lai, A. C. K., and Nazaroff, W. W., Modeling indoor particle deposition from
turbulent air flow onto smooth surfaces, Journal of Aerosol Science, 2000,31, 463-
476.
12. Fogh, C. L., Byrne, M. A., Roed, J., and Goddard, A. J. H., Size specific indoor
aerosol deposition measurements and derived I/O concentrations ratios, Atmospheric
Environment, 1997,3;.- 2193-2203.
15
-------
13. Goddard, A. J. H., Byrne, M. A., Lange, C., and Roed, J., Aerosols indoors:
deposition on indoor surfaces, Air Infiltration Review, 1995,16(2): 1:4.
14. Byrne, M. A., Goddard, A. J. H., Lockwood, F. C., and Nasrullah, M., Partieulate
deposition on indoor surfaces—its role, with ventilation, in indoor air quality
prediction, Implementing the Results of Ventilation Research, 16th AJVC Conference,
. Palm Springs, CA, September, 19-22, 1995.
15. Sparks, L. E., Mosley, R. B., and Guo, Z., Deposition rates of particles indoors as a
function of particle diameter (poster), PM 2000: Partieulate Matter and Health—The
Scientific Basis for Regulatory Decision-making, Charleston, SC, January 24-28,
2000.
16. Hanley, J. T., Ensor, D. S., Smith, D. D., and Sparks, L. E., Fractional aerosol
filtration efficiency of in-duct ventilation air cleaners, Indoor Air,l994,4:3,169-178.
17. American Society for Testing and Materials standard guide for evaluation of indoor
air quality models, D515 7-91, American Society for Testing and Materials,
Philadelphia, PA, 1991.
16
-------
Keywords
indoor air quality, model, particulate matter, indoor particulate, indoor/outdoor ratio
1.7
-------
NRMRL- RTP-P-524
TECHNICAL REPORT DATA
{Pl/mst read luttivttions <*» the tottne
1.
NO,
EPA/600/A-OQ/055
4, T)TLE AND 5USTI TC_e
An Indoor Air Quality Model for Participate Matter
REPORT DATE
t. AUTHORtst
Leslie E, Sparks
8.
ORGANIZATION REPORT NO.
9. FE WORMING ORGANIZATION NAME AND ADDRESS
See Block 12
11. CONTRACT/gRANT MO,
N.A (Inhouse)
J3, SPONSQRtNG AGENCY NAME AMD ADDRESS
EPA, Office of Research and
Air Pollution Prevention and Control Division
Research Triangle Park, NC 277U
13. TVPE OF nePGftT AND PERIOD COVERED
Published paper; 1-6/00
14. SFOMSORINf, AGENCY
EPA/600/13
APPCDproject officer is Leslie E. Sparks, Mail Drop 54, 919/
541-2458. For presentation at AWMA/EPA Conference. Engineering Solutions to
Indoor Air Quality Problems, Raleigh,' NC, 7/17-19/00.
The paper discusses an indoor air quality (IAQ) model for participate mat"
ter (PM). The standard for PM < 2.5 xiucrometers in aerodynamic diameter (PM
2. 5) proposed by the U. S. EPA has produced considerable interest in. indoor expo-
sures to PM. IAQ. models provide a useful tool for analyzing both the indoor expo-
sure to PM and the impact of risk management options on exposure. Because analy-
sis of the impact of PM exposures requires analysis over a particle size distribution
a?osI existing LAQ models, whicii are designed to alluw cuialysie of the impact of a
single pollutant component, are not well suited for analysis of PM exposure. To
overcome this limitation, a multicompartment f-^Q model for PM exposures for a
full particle size distribution was developed. The model allows analysis of the effect
of: the building shell on the penetration of outdoor particles into ihe indoors, the
deposition of particles to indoor surfaces, particle removal by air r-]efinr>rK* and in-
door particle sources. The use of the model is demonstrated by an analysis of both
the time-varying impact of outdoor PM on indoor KM levels and the effect of a cen-
tral furnace filter on indoor PM concentrations.
KEY WORDS A«0 DOCUMENT ANAUV3IS
PESCHIPTORS
END6O TERMS
Pollution
Particles
Air Filters
Pollution Control
Stationary Sources
Exposure
Analyzing
Air Cleaners
Indoor Air Quality
Fwld/G(i«ip
13B
14G
12A
63
14B
ISA, 131
13K
18, QiSTFltBUTION STATEMENT
Release to Public
14. SECURITY CLASS
Unclassified
21, NO. OP PAGES
17
M.SECUHITV
Unclassified
22,
EPA Farm
(3-73|
------- |